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The finite element solution of a quasi-linear elliptic equation governing non-Newtonian flows through rectangular ducts. (English) Zbl 0584.76005

A Rayleigh-Ritz finite element method (FEM) using quadratic, cubic and quartic elements has been used to solve the steady laminar flow of a non- Newtonian fluid through rectangular ducts. Different iterative approaches were investigated to solve the large system of linear equations resulting from the discretization of the quasi-linear partial differential equation. The performance of the FEM incorporating the method of variation of parameters (Davidenko path procedure [D. F. Davidenko, Dokl. Akad. Nauk SSSR 88, 601-602 (1953; Zbl 0050.121)]) was compared with the finite difference method in terms of speed, accuracy and the capability of handling the very pronounced nonlinearity. From the convergent solutions obtained, some flow parameters were investigated. The results presented agree well with other published work.

MSC:

76A05 Non-Newtonian fluids
76M99 Basic methods in fluid mechanics

Citations:

Zbl 0050.121

Software:

TWODEPEP
PDFBibTeX XMLCite
Full Text: DOI

References:

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This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.